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I’ll give you a simple assignment. The United States is filled with depleted oil fields, from New York to California, Alaska to Texas. The fields are there because they are traps of varying types. Anticlines, fault-line, unconformity, stratigraphic, etc. Show me one of them that has suddenly been recharged and then returns to flush production. Just one.

I don't think any of them have been re-charged. There are a host of factors which can contribute to them becoming productive again, most of which relate to how they were produced in the first place. Most reservoirs contain water and oil, and producing any reservoir too fast will cause the well to 'cone in', wetting the near bore porosity with water, and causing the well to produce more water than oil.

Water generally is less viscous than oil.

That may give the impression the oil has been produced, and it has, near the wellbore, but that leaves a lot of oil left in the reservoir. Horizontal wells will get that oil at a greater efficiency, but only when the well is drilled in the right part of the formation and produced correctly. Some things can't be rushed.

Another factor in apparent reservoir depletion is having reached bubble point, where natural gas dissolved in the oil comes out of solution in the reservoir rock, blocking pore throats and causing oil production to drop off. Maintaining reservoir pressure can prevent this, restoring it through injection of production water might cause the problem to clear up, but that is secondary recovery.

Often, what makes a well or field viable is economics: the cost of operating the wells plus the cost of disposing of produced water and cost of transporting oil to market versus the revenue generated by the oil, with costs for well maintenance and eventual site reclamation factored in.

If it won't make money, it will sit where it is, for the most part.

I did hear of an offshore well which gave the appearance of recharging, but it turned out the oil was coming from a deeper reservoir along either fault lines or fractures.

So, nope, no recharge, just the occasional rearrangement of fluids in badly produced reservoirs.

Is that how it has to work, and with that timing?